Dynamical Study of Newly Created Analytical Solutions, Bifurcation Analysis, and Chaotic Nature of the Complex Kraenkel–Manna–Merle System

Rani, Setu; Kumar, Sachin; Kumar, Raj

doi:10.1007/s12346-024-01148-z

Qual. Theory Dyn. Syst.

2024

DOI: 10.1007/s12346-024-01148-z

|View full text |Cite

Dynamical Study of Newly Created Analytical Solutions, Bifurcation Analysis, and Chaotic Nature of the Complex Kraenkel–Manna–Merle System

Setu Rani,

Sachin Kumar,

Raj Kumar

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Bifurcation, Chaotic Behavior and Effects of Noise on the Solitons for the Stochastic Jaulent-Miodek Hierarchy Model

Baber,

Shahzad,

Munir

et al. 2024

Int J Theor Phys

View full text Add to dashboard Cite

Bifurcation, Chaotic Behavior and Effects of Noise on the Solitons for the Stochastic Jaulent-Miodek Hierarchy Model

Baber,

Shahzad,

Munir

et al. 2024

Int J Theor Phys

View full text Add to dashboard Cite

Comparative study of novel solitary wave solutions with unveiling bifurcation and chaotic structure modelled by stochastic dynamical system

Alazman,

Narayan Mishra,

Alkahtani

et al. 2024

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

In this study, we conduct a comprehensive investigation of the novel characteristics of the (2 + 1)-dimensional stochastic Hirota–Maccari System (SHMS), which is a prominent mathematical model with significant applications in the field of nonlinear science and applied mathematics. Specifically, SHMS plays a critical role in the study of soliton dynamics, nonlinear wave propagation, and stochastic effects in complex physical systems such as fluid dynamics, optics, and plasma physics. In order to account for the abrupt and significant fluctuation, the aforementioned system is investigated using a Wiener process with multiplicative noise in the Itô sense. The considered equation is studied by the new extended direct algebraic method (NEDAM) and the modified Sardar sub-equation (MSSE) method. By solving this equation, we systematically derived the novel soliton solutions in the form of dark, dark-bright, bright-dark, singular, periodic, exponential, and rational forms. Additionally, we also categorize and analyze the W-shape, M-shape, bell shape, exponential, and hyperbolic soliton wave solutions, which are not documented by researchers. The bifurcation, chaos and sensitivity analysis has been depicted which represent the applicability of the system in different dynamics. These findings greatly advance our knowledge of nonlinear wave events in higher-dimensional stochastic systems both theoretically and in terms of possible applications. These findings are poised to open new avenues for future research into the applicability of stochastic nonlinear models in various scientific and industrial domains.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Dynamical Study of Newly Created Analytical Solutions, Bifurcation Analysis, and Chaotic Nature of the Complex Kraenkel–Manna–Merle System

Cited by 2 publications

References 44 publications

Bifurcation, Chaotic Behavior and Effects of Noise on the Solitons for the Stochastic Jaulent-Miodek Hierarchy Model

Bifurcation, Chaotic Behavior and Effects of Noise on the Solitons for the Stochastic Jaulent-Miodek Hierarchy Model

Comparative study of novel solitary wave solutions with unveiling bifurcation and chaotic structure modelled by stochastic dynamical system

Contact Info

Product

Resources

About